Let S be a non-empty subset of R. Consid...

Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number `x in S` such that `x"">""0`.
Which of the following statements is the negation of the statement P ?
There is no rational number `x in S` such that `xlt=0` (9)
Every rational number `x in S` satisfies `xlt=0` (18)
`x in S` and `xlt=0=>x` (27) is not rational
There is a rational number `x in S` such that `xlt=0` (36)

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`x in S`
`x > 0`
`x in S; x <= 0`
option 2 is correct

Let S be non-empty subset of R. consider the following statement: P: There is a rational number x ne S " such that " x gt 0 Which of the following statements is the negation of the statement P ?

Every rational number `x ne S ` such that `x le 0`

`x in S and x le 0 Rightarrow x` is not rational

There is a rational number `x in S " such that " x le 0`

There is no rational number `x in S " such that x le 0`

`x in S` and `x le 0 rArr x` is not rational

There is rational number `x in S` such that `xle0`.

There is no rational number `x in S` such that `xle0`.

Every rational number `x in S` satisfies `xle0`

There is a rational number `x in S` such that `x le 0`

There is no rational number `x in S` such that `x le 0`

Every rational number `x in S` satisfies `x le 0`

`x in S` and `x le 0 rArr x` is not rational